MinT - Best Known (109, 109+41, s)-Nets in Base 4

Best Known (109, 109+41, s)-Nets in Base 4

(109, 109+41, 531)-Net over F₄ — Constructive and digital

Digital (109, 150, 531)-net over F₄, using

3 times m-reduction [i] based on digital (109, 153, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 51, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(109, 109+41, 971)-Net over F₄ — Digital

Digital (109, 150, 971)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+41, 84615)-Net in Base 4 — Upper bound on s

There is no (109, 150, 84616)-net in base 4, because

1 times m-reduction [i] would yield (109, 149, 84616)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 509342 062556 741565 973869 927236 626285 460810 539940 923355 826731 611855 691545 805282 216842 816744 > 4¹⁴⁹ [i]